Process Capability or Quality Compliance Assessment

Evaluate whether a production process or system meets a specified quality/compliance target by computing normal probabilities and comparing to a threshold, often involving a process capability index.

csat-suneung 2010 Q9 4 marks View
The internal pressure strength of bottles produced at a certain factory follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$, and bottles with internal pressure strength less than 40 are classified as defective. The process capability index $G$ for evaluating the factory's process capability is calculated as $$G = \frac { m - 40 } { 3 \sigma }$$ When $G = 0.8$, what is the probability that a randomly selected bottle is defective, using the standard normal distribution table on the right? [4 points]
$z$$\mathrm { P } ( 0 \leqq Z \leqq z )$
2.20.4861
2.30.4893
2.40.4918
2.50.4938

(1) 0.0139
(2) 0.0107
(3) 0.0082
(4) 0.0062
(5) 0.0038
csat-suneung 2010 Q9 4 marks View
The internal pressure strength of bottles produced at a certain factory follows a normal distribution $\mathrm { N } \left( m , \sigma ^ { 2 } \right)$, and bottles with internal pressure strength less than 40 are classified as defective. The process capability index $G$ for evaluating the process capability of this factory is calculated as $$G = \frac { m - 40 } { 3 \sigma }$$ When $G = 0.8$, what is the probability that a randomly selected bottle is defective, using the standard normal distribution table below? [4 points]
$z$$\mathrm { P } ( 0 \leqq Z \leqq z )$
2.20.4861
2.30.4893
2.40.4918
2.50.4938

(1) 0.0139
(2) 0.0107
(3) 0.0082
(4) 0.0062
(5) 0.0038